The distribution of Votaw’s λ1（vc） criterion for testing compound symmetryof the covariance matrix of a t-variate Gaussian model has been obtained in terms ofMeijer’s G-function as well as in computable series fo...The distribution of Votaw’s λ1（vc） criterion for testing compound symmetryof the covariance matrix of a t-variate Gaussian model has been obtained in terms ofMeijer’s G-function as well as in computable series form. Special cases of the densityhave also been derived using reduction formulae for G-function.展开更多
The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily, for symmetric p...The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily, for symmetric positive definite random matrices, this ratio can take various forms and its distribution, and even its definition, can offer many challenges. However, for the distribution of its determinant, Meijer G-function often provides an effective analytic and computational tool, applicable at any division level, because of its reproductive property.展开更多
For the case where the multivariate normal population does not have null correlations, we give the exact expression of the distribution of the sample matrix of correlations R, with the sample variances acting as param...For the case where the multivariate normal population does not have null correlations, we give the exact expression of the distribution of the sample matrix of correlations R, with the sample variances acting as parameters. Also, the distribution of its determinant is established in terms of Meijer G-functions in the null-correlation case. Several numerical examples are given, and applications to the concept of system de- pendence in Reliability Theory are presented.展开更多
文摘The distribution of Votaw’s λ1（vc） criterion for testing compound symmetryof the covariance matrix of a t-variate Gaussian model has been obtained in terms ofMeijer’s G-function as well as in computable series form. Special cases of the densityhave also been derived using reduction formulae for G-function.
文摘The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily, for symmetric positive definite random matrices, this ratio can take various forms and its distribution, and even its definition, can offer many challenges. However, for the distribution of its determinant, Meijer G-function often provides an effective analytic and computational tool, applicable at any division level, because of its reproductive property.
文摘For the case where the multivariate normal population does not have null correlations, we give the exact expression of the distribution of the sample matrix of correlations R, with the sample variances acting as parameters. Also, the distribution of its determinant is established in terms of Meijer G-functions in the null-correlation case. Several numerical examples are given, and applications to the concept of system de- pendence in Reliability Theory are presented.
